Block #1,736,129

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/27/2016, 8:06:37 AM · Difficulty 10.7175 · 5,095,612 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

44f660f2c685f156c49db3f5affcdf556fb8d586a112835f4db85cb48f58fc02

View on Chainz ↗

Height

#1,736,129

Difficulty

10.717514

Transactions

Size

2.58 KB

Version

Bits

0ab7aefc

Nonce

848,895,769

Timestamp

8/27/2016, 8:06:37 AM

Confirmations

5,095,612

Mined by

⛏️ P2SHAL4uLFMYgMFMc1PUtriwVT8d5p5MMEAriM

Merkle Root

57072cd74bada7ae0fd143f10d2c7c3cb4a51b80c21c8824ef833e3b5b7686b0

Transactions (2)

Coinbase496184b1536765…14d49f9fe6e56d

1 in → 1 out8.7300 XPM110 B

AL4uLFMY…5MMEAriM

ffbf31cfc72b79…dbff1bcaccbc06

16 in → 2 out4.9100 XPM2.39 KB

AWPvLEeT…xSmKE15z AGCdb3gj…7saDgdNm

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.824 × 10⁹⁵(96-digit number)

38245155360909220608…08109705574307810559

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

3.824 × 10⁹⁵(96-digit number)

38245155360909220608…08109705574307810559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.824 × 10⁹⁵(96-digit number)

38245155360909220608…08109705574307810561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.649 × 10⁹⁵(96-digit number)

76490310721818441217…16219411148615621119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.649 × 10⁹⁵(96-digit number)

76490310721818441217…16219411148615621121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.529 × 10⁹⁶(97-digit number)

15298062144363688243…32438822297231242239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.529 × 10⁹⁶(97-digit number)

15298062144363688243…32438822297231242241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.059 × 10⁹⁶(97-digit number)

30596124288727376486…64877644594462484479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.059 × 10⁹⁶(97-digit number)

30596124288727376486…64877644594462484481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

6.119 × 10⁹⁶(97-digit number)

61192248577454752973…29755289188924968959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.119 × 10⁹⁶(97-digit number)

61192248577454752973…29755289188924968961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,736,129

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